SOLUTION: Soybean meal is 16% protein and cornmeal is 8% protien, how many pounds of each should be mixed together in order to get 320lb mixture that is 13% protein?

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Question 178279: Soybean meal is 16% protein and cornmeal is 8% protien, how many pounds of each should be mixed together in order to get 320lb mixture that is 13% protein?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a= pounds of soybean meal needed
Let b= pounds of cornmeal needed
In words:
(pounds of protein in soybean meal + pounds of protein in cornmeal) /
(total pounds of soybean and cornmeal) = % protein
given:
(1) a+%2B+b+=+320
(2) %28.16a+%2B+.08b%29%2F%28a+%2B+b%29+=+.13
%28.16a+%2B+.08b%29%2F320+=+.13
.16a+%2B+.08b+=+.13%2A320
(3).16a+%2B+.08b+=+41.6
Multiply both sides of (1) by .08 and subtract from (3)
(3) .16a+%2B+.08b+=+41.6
(1) -.08a+-+.08b+=+-25.6
.08a+=+16
a+=+200
And, since
(1) a+%2B+b+=+320
200+%2B+b+=+320
b+=+120
200 pounds of soybean meal are needed and
120 pounds of cornmeal are needed
check:
(2) %28.16a+%2B+.08b%29%2F%28a+%2B+b%29+=+.13
%28.16%2A200+%2B+.08%2A120%29%2F320+=+.13
%2832+%2B+9.6%29%2F320+=+.13
41.6%2F320+=+.13
41.6+=+41.6
OK